I’ve just finished my lectures for the course in Fourier Series and Fourier Transforms that I’ve been teaching.

It was an intense, exhilarating and ultimately frustrating three-and-a-half week adventure –and I fear that it didn’t go very well. It’s tough material, probably the first stuff that these second-year students have seen in their undergraduate career that’s really brand new to them. And, of course, this was my first time teaching it so our combined inexperience didn’t exactly presage a “positive learning outcome”.

What did I learn, then?

• Precision counts: I made my fair share of mistakes, mostly just typos, but those are easy for me to correct or even ignore, much harder for the 180 other people in the room who don’t already understand the material.
• Organization counts: actually, my lectures were highly structured, but I don’t think that always came through as I spoke. Explicit (numbered sections, bullet points, real sentences) is better than implicit.
• Preparation counts: In principle all of us lecturers know what the student have already learned, but just because something has been on on a syllabus doesn’t mean they really understand. Particularly with math, I think we often expect a level of facility that comes with years and years of practice doing integrals, solving equations, getting used to unfamiliar notation, that the students don’t yet have. (Needless to say, we’re usually convinced that things were better when we were in their place, but I’m not always so sure, as we look back with our rose-tinted shades.)

Still, I did some things right. The students may disagree, but I think I actually did a reasonable job at explaining the material in a way that isn’t just copying from the books. Perhaps that’s why my lecture notes seem to be more popular than the lectures themselves. And at least my loud Yankee voice carries to the back of the room.

Feedback is, of course, welcome.

p.s. On a more amusing note (purposely buried down here, free of links), it looks like Imperial Astrophysics is going to be getting a very special new (-ish) graduate student soon.